Future directions: magnon probes and spin flips

We have successfully demonstrated the coherent control of ultrafast spin precession in antiferromagnetic NiO using the Zeeman torque of an intense THz transient. Such a control scheme is minimally invasive (as it leaves the non-spin degrees of freedom of the NiO in their ground state) and universal (as it is mediated by the Zeeman interaction). Coherent magnons may now be used as probes for ultrafast interactions of electron spin with orbital motion and lattice modes in essentially all THz-transparent matter and at all relevant frequencies.

We emphasize that Zeeman-driven spin motion is expected to be widely scalable, and our simulations based on equation (7) indicate a novel regime of dramatic THz nonlinearities beyond the perturbative regime. In contrast to the weak-field regime (figure7(a)), THz peak amplitudes of 11 T lead to oscillations ofS_1x significantly slower than the high-frequency magnon at 1 THz, and the evolution of S_1y is dominated by the low-frequency magnon at≈0.2 THz (figure7(b)).

Note that both signals exhibit a modulation depth of nearly 100 %. Most remarkably, the change of S_1z from 1 to nearly −1 demonstrates the induction of a spin flip, which also becomes apparent in an image of the three-dimensional spin trajectory (figure7(d)). It is not obvious whether in such an extreme excitation regime the parameters of the spin Hamiltonian of equation (6) can still be assumed to be constant. However, recent modeling based on an extended Hamiltonian has demonstrated similar magnetization dynamics [52]. In any case, future studies of high-field-driven THz spin dynamics will enter an entirely new territory of many-body physics.

15

Figure 7. Simulated dynamics of sublattice spin S₁ (a) under the excitation conditions used in the experiment (peak driving field 0.14 T) and (b) with a peak field of 11 T. (c, d) Three-dimensional spin trajectories resulting from (a) and (b), respectively. In (c), spin deflections are numerically enhanced for better visibility.

4. Conclusions and perspectives

Intense electric and magnetic multi-THz fields have become versatile tools to selectively and coherently control electronic or spin degrees of freedom of condensed matter in a previously elusive spectral range, and in the sub-optical-cycle temporal regime. Our study of multi-THz two-dimensional spectroscopy confirms the onset of a non-perturbative response under even off-resonant excitation of interband transitions in InSb. Peak electric fields above 5 MV cm⁻¹ lead to carrier-wave Rabi flopping between the valence and conduction bands. These results underpin the large potential of novel strong-field multi-THz technology for high harmonics generation [53] and coherent quantum control of low-energy excitations [22, 54]. The unique capability of field-sensitive multi-dimensional spectroscopy to separate purely coherent and incoherent nonlinearities may open a new chapter in the investigation of collective low-energy excitations including inter-molecular vibrations in hydrogen-bonded liquids [55] and Cooper pair breaking transitions in superconductors [56]. On the other hand, all-magnetic spin control opens the door to the new concept of THz electron spin resonance. Coherent magnons in systems as diverse as ferro- and antiferromagnets or high-temperature superconductors may, for instance, be employed as unique probes of ultrafast interactions with lattice and charge degrees of freedom. Furthermore, our experiments may inspire the development of ultrafast next-generation memory devices, spin-based quantum computation and spintronics. This is only the beginning of a new era of sub-cycle multi-THz coherent control of condensed matter.

Acknowledgments

We thank A Leitenstorfer, M Wolf, M Fiebig, B Mayer, O Schubert, F Junginger, S M¨ahrlein, C Schmidt, G Klatt and T Dekorsy for ongoing collaborations which laid the basis for this work. We also appreciate fruitful discussions with T Cocker, D Seletskiy, M P Hasselbeck and M Sheik-Bahae. Financial support by Deutsche Forschungsgemeinschaft (DFG) through projects PA 2113/1-1 and HU 1598/1-1 as well as by the European Research Council via ERC Starting Grant QUANTUMsubCYCLE is gratefully acknowledged.

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